How do you write an essay on a character without just being descriptive?

I think there are two key points to this answer. Firstly, that though a question may just say 'discuss character X', what its really asking is 'how does character X develop' - its very rare to find a totally unchanging character in a novel or play, and near on impossible that the exam board would ask you a question on such a character - thus what you need to look for a moments of change. Go through the relevant plotline for the character in question and identify the key moments in which their attitudes and world-views are altered. These turning points become the basis of your essay because its now your job to explain why the character changes, how they change, and then, most importantly, how the author presents these changes through their choice of language before. This works because if you focus intensely on moments of change, particularly the presentation of these moments, you naturally narrow your scope, looking at specific passages rather than vast swathes of a work (which often results in being descriptive), and doing so in a critical way. Secondly, and though this may seem obvious it is essential to analysing these moments, just because the question names one character does not mean you only talk about that character. The best way to truly analyse change is examining how the character's views towards and interactions with other characters change; how they express themselves and their intentions differently because of the changing moment. Indeed, only referencing the named character and not focusing enough on their interactions with others is what can very easily lead to description. This is because you can end up over simplifying the novel/play in your mind, thinking of the named character in isolation, and not as the result of their politically, emotionally, and socially complex world.